Hi, I've got one as well, a nearly mint condition 516/2, and I also have puzzling over this camera. As you know, it is an oddity in the Nettar line-up, being the first Nettar with double-exposure prevention and the last one with a pop-up viewfinder. Mine was apparently produced in about 1942 (the date of the lens) using a shutter from 10 years earlier, possibly raiding old stock because of wartime shortages.
This week I happened to glance at the more up-market Zeiss Ikonta and - lo and behold - it turns out that the 516/2 Nettar is indistinguishable from the (West German) Ikonta 521/2 first released in 1947. It is also almost indistinguishable from the (East German) Ercona I, which appears to have been the same as the 521/2. The only difference I can make out is that the Ercona and at some (not all) 521s seem to have a button next to the viewfinder which presumably flicks it up.
Beyond that, it is all speculation. I wonder if the 516 was intended as the next generation of Nettars but was redeployed as an Ikonta when Zeiss was casting around for a new look Ikonta in 1946. I can't think of another sensible reason why an original Nettar design would reappear a few years later with the Ikonta badge. There are so few 516s around that I wonder if they were a prototype that never went into full production.
The first post-war Nettar, the Nettar II, didn't go into production until 1949 (according to Camerapedia), two years after the Ikonta 521, and had a redesigned top-plate with the built-in viewfinder but the 517 did not have the double-exposure lock so it was actually a step back from the 516. The 518 "signal Nettar" also came out in '49, and is usually (and we know, wrongly) described as the first Nettar with double-exposure prevention.
I do wonder if the 516 is not mentioned in the lists is that it may never have been produced commercially, perhaps there were a handful of prototypes made before more pressing wartime jobs claimed Zeiss's attention.
IT is all speculation, as I said, but clearly we are in possession of genuinely rare versions of an otherwise common camera.